Question

The first four terms of a sequence are shown on the graph below.

What can be concluded about the sequence?
The common ratio of the sequence is 2.
The common difference of the sequence is 2.
The next term of the sequence is represented by the point (5, 64).
The next term of the sequence is represented by the point (5, –64).

Answer 1

The next term of the sequence is represented by the point (5, –64)

Explanation:

From inspection of the graph, the first four terms of the sequence are:

• (1, -4)
• (2, 8)
• (3, -16)
• (4, 32)

Each x-value increases by 1 for each consecutive term.

Each y-value is the previous y-value multiplied by -2.

Therefore, it is a geometric sequence with a common ratio of -2.

Following the above rule, if the last term in the sequence is (4, 32), then the next term in the sequence will be:

• x = 4 + 1 = 5
• y = 32 × -2 = -64

So, the next term of the sequence is represented by the point (5, –64)